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9^n - 5^n + 1.
19

%I #14 Jun 13 2015 00:52:47

%S 1,5,57,605,5937,55925,515817,4704845,42656097,385467365,3477018777,

%T 31332231485,282185395857,2540645125205,22870688939337,

%U 205860614516525,1852867600961217,16676418760213445,150090820599733497

%N 9^n - 5^n + 1.

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (15,-59,45).

%F G.f.: 1/(1-9*x)-1/(1-5*x)+1/(1-x). E.g.f.: e^(9*x)-e^(5*x)+e^x.

%F a(n)=14*a(n-1)-45*a(n-2)+32 with a(0)=1, a(1)=5 [From _Vincenzo Librandi_, Jul 21 2010]

%o (PARI) a(n)=9^n-5^n+1 \\ _Charles R Greathouse IV_, Dec 22 2011

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Jan 30 2009